Let $F=\mathbb Z/(p)$, where $p$ a prime number, $f(x)$ a monic irreducible polynomial in $K=F[x]$ of degree $n$, $K=F[x]/(f(x))$, and $E$ the multiplicative group of nonzero elements of $K$. Then it is easy to see that $K=F(x+f(x))$. Is $x+(f(x))$ a generator of $E$ as a multiplicative group?

i want to know under what condictions , $x + (f(x))$ is a generator
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Aimin XuDec 3 '13 at 8:18

@AiminXu You have to compute the multiplicative order of $x + (f(x))$, like I did above. Like for irreducibility, in general there is no "easier" way to check if a polynomial is primitive.
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azimutDec 3 '13 at 8:21